Here we briefly examine the time complexity of the quantum algorithm excluding the classical computing components. Following the analysis of the variational Poisson solver [1]}, the time complexity of the proposed variational evolution equation solver per time-step reads
\(T \sim \mathcal {O}\left(\bar{T}_{\mathrm {eval}}\left(\frac{l+e+n^{2}}{\varepsilon ^{2}}\right)\right),\) 
